Find the z-score for each score in the population. Round each of your z-scores to two decimal places. Then, transform the original population into a new population of N = 4 scores with a u = 1000 and a o 200. Use the rounded z-scores (to two decimal places) to calculate the new scores. Complete the following chart using the values that you found: Z Xoriginal population Xnew population *2 decimal places* 66 84 42 68

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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What is the z score for each score? Round to two decimal places. Then transform the original population into a new population of N=4 scores with a u=1000 and o=200. Use to calculate new scores!
**Instructions for Calculating and Transforming Z-Scores**

**Task:**

1. **Find the z-score** for each score in the original population. Round each of your z-scores to two decimal places.

2. **Transform the original population** into a new population composed of N = 4 scores with a mean (μ) of 1000 and a standard deviation (σ) of 200. Use the rounded z-scores (to two decimal places) to calculate the new scores.

**Chart Completion:**

Complete the following chart using the values that you found:

| \( X_{\text{original population}} \) | \( z \) (2 decimal places) | \( X_{\text{new population}} \) |
|--------------------------------------|--------------------------|-------------------------------|
| 66                                   |                          |                               |
| 84                                   |                          |                               |
| 42                                   |                          |                               |
| 68                                   |                          |                               |

**Guidelines:**

- Calculate each z-score using the formula:
  \[
  z = \frac{(X - \mu)}{\sigma}
  \]

- After obtaining all the z-scores, convert back to the new population scores using the transformation:
  \[
  X_{\text{new}} = z \cdot \sigma_{\text{new}} + \mu_{\text{new}}
  \]

- Ensure all calculations are accurate and rounded correctly before inputting into the chart.
Transcribed Image Text:**Instructions for Calculating and Transforming Z-Scores** **Task:** 1. **Find the z-score** for each score in the original population. Round each of your z-scores to two decimal places. 2. **Transform the original population** into a new population composed of N = 4 scores with a mean (μ) of 1000 and a standard deviation (σ) of 200. Use the rounded z-scores (to two decimal places) to calculate the new scores. **Chart Completion:** Complete the following chart using the values that you found: | \( X_{\text{original population}} \) | \( z \) (2 decimal places) | \( X_{\text{new population}} \) | |--------------------------------------|--------------------------|-------------------------------| | 66 | | | | 84 | | | | 42 | | | | 68 | | | **Guidelines:** - Calculate each z-score using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] - After obtaining all the z-scores, convert back to the new population scores using the transformation: \[ X_{\text{new}} = z \cdot \sigma_{\text{new}} + \mu_{\text{new}} \] - Ensure all calculations are accurate and rounded correctly before inputting into the chart.
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